Question $2[25$ marks$]$

$2\mathrm{.}1.$ If Locos Consulting Engineers Pty Ltd has made an investment of R$450000$ in a property and received R$750000$ five years later. Determine the rate of return? $(10$ marks$)$

$2\mathrm{.}2.$ An electrical engineer in from Locos Consulting Engineers Pty Ltd wants to deposit an amount $P$ now such that she can withdraw an equal annual amount of $A1=$ R$2000$ per year for the first $5$ years, starting $1$ year after the deposit, and a different annual withdrawal of $A2=R3000$ per year for the following $3$ years. How would the cash flow diagram appear if $i=8\mathrm{.}5\%$ per year? $(10$ marks$)$

$2\mathrm{.}3.$ Last year Locos Consulting Engineers Pty Ltd invested in the US using dollars currency, the company offered to put enough money into a savings account to generate $$5000$ in interest this year to assist in growing the company's investments. $($a$)$ Identify the symbols, and $($b$)$ calculate the amount that had to be deposited exactly $1$ year ago to earn $$5000$ in interest now, if the rate of return is $6\%$ per year. $(10$ marks$)$